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Using more than a million randomly generated equations of state that satisfy theoretical and observational constraints, we construct a novel, scale-independent description of the sound speed in neutron stars, where the latter is expressed in a unit cube spanning the normalized radius, r/R, and the mass normalized to the maximum one, M/MTOV. From this generic representation, a number of interesting and surprising results can be deduced. In particular, we find that light (heavy) stars have stiff (soft) cores and soft (stiff) outer layers, or that the maximum of the sound speed is located at the center of light stars but moves to the outer layers for stars with M/MTOV ≳ 0.7, reaching a constant value of cs = 1 2 2 as M → MTOV. We also show that the sound speed decreases below the conformal limit cs = 1 3 2 at the center of stars with M = MTOV. Finally, we construct an analytic expression that accurately describes the radial dependence of the sound speed as a function of the neutron-star mass, thus providing an estimate of the maximum sound speed expected in a neutron star.
In the initial stage of relativistic heavy-ion collisions, strong magnetic fields appear due to the large velocity of the colliding charges. The evolution of these fields appears as a novel and intriguing feature in the fluid-dynamical description of heavy-ion collisions. In this work, we study analytically the one-dimensional, longitudinally boost-invariant motion of an ideal fluid in the presence of a transverse magnetic field. Interestingly, we find that, in the limit of ideal magnetohydrodynamics, i.e., for infinite conductivity, and irrespective of the strength of the initial magnetization, the decay of the fluid energy density e with proper time τ is the same as for the time-honoured “Bjorken flow” without magnetic field. Furthermore, when the magnetic field is assumed to decay , where a is an arbitrary number, two classes of analytic solutions can be found depending on whether a is larger or smaller than one. In summary, the analytic solutions presented here highlight that the Bjorken flow is far more general than formerly thought. These solutions can serve both to gain insight on the dynamics of heavy-ion collisions in the presence of strong magnetic fields and as testbeds for numerical codes.
We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state of neutron stars employing either variable- or constant-likelihood functions. The former have the advantage that it retains the full information on the distributions of the measurements, making an exhaustive usage of the data. The latter, on the other hand, have the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound-speed parameterization method so as to satisfy the constraints from X-ray and gravitationalwaves observations, as well as those from Chiral Effective Theory and perturbative QCD. In all cases, the two approaches lead to very similar results and the 90%-confidence levels are essentially overlapping. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff set on the binary tidal deformability Λ˜ ≤ 720 employed in the constant-likelihood analysis. Our analysis has also produced two additional results. First, a clear inverse correlation between the normalized central number density of a maximally massive star, nc,TOV/ns, and the radius of a maximally massive star, RTOV. Second, and most importantly, it has confirmed the relation between the chirp mass Mchirp and the binary tidal deformability Λ˜. The importance of this result is that it relates a quantity that is measured very accurately, Mchirp, with a quantity that contains important information on the micro-physics, Λ˜. Hence, once Mchirp is measured in future detections, our relation has the potential of setting tight constraints on Λ˜.
We have investigated the systematic differences introduced when performing a Bayesian-inference analysis of the equation of state (EOS) of neutron stars employing either variable- or constant-likelihood functions. The former has the advantage of retaining the full information on the distributions of the measurements, making exhaustive usage of the data. The latter, on the other hand, has the advantage of a much simpler implementation and reduced computational costs. In both approaches, the EOSs have identical priors and have been built using the sound speed parameterization method so as to satisfy the constraints from X-ray and gravitational waves observations, as well as those from chiral effective theory and perturbative quantum chromodynamics. In all cases, the two approaches lead to very similar results and the 90% confidence levels essentially overlap. Some differences do appear, but in regions where the probability density is extremely small and are mostly due to the sharp cutoff on the binary tidal deformability L˜ 720 set in the constant-likelihood approach. Our analysis has also produced two additional results. First, an inverse correlation between the normalized central number density, nc,TOV/ns, and the radius of a maximally massive star, RTOV. Second, and most importantly, it has confirmed the relation between the chirp mass and the binary tidal deformability. The importance of this result is that it relates chirp, which is measured very accurately, and L˜ , which contains important information on the EOS. Hence, when chirp is measured in future detections, our relation can be used to set tight constraints on L˜ .
The amplification of magnetic fields plays an important role in explaining numerous astrophysical phenomena associated with binary neutron star mergers, such as mass ejection and the powering of short gamma-ray bursts. Magnetic fields in isolated neutron stars are often assumed to be confined to a small region near the stellar surface, while they are normally taken to fill the whole star in numerical modeling of mergers. By performing high-resolution, global, and high-order general-relativistic magnetohydrodynamic simulations, we investigate the impact of a purely crustal magnetic field and contrast it with the standard configuration consisting of a dipolar magnetic field with the same magnetic energy but filling the whole star. While the crust configurations are very effective in generating strong magnetic fields during the Kelvin–Helmholtz-instability stage, they fail to achieve the same level of magnetic-field amplification of the full-star configurations. This is due to the lack of magnetized material in the neutron-star interiors to be used for further turbulent amplification and to the surface losses of highly magnetized matter in the crust configurations. Hence, the final magnetic energies in the two configurations differ by more than 1 order of magnitude. We briefly discuss the impact of these results on astrophysical observables and how they can be employed to deduce the magnetic topology in merging binaries.
We investigate the effect of large magnetic fields on the (2 + 1)-dimensional reduced-magnetohydrodynamical expansion of hot and dense nuclear matter produced in √sNN = 200 GeV Au+Au collisions. For the sake of simplicity,we consider the casewhere themagnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time (τ ) for the case of zero electrical conductivity of the QGP is parametrized following Deng et al. [Phys. Rev. C 85, 044907 (2012)], and for finite electrical conductivity following Tuchin [Phys. Rev. C 88, 024911 (2013)].We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with nonzero impact parameter we observe considerable changes in the evolution of the momentum eccentricities of the fireball when comparing the case when the magnetic field decays in a conducting QGP medium and when no magnetic field is present. The elliptic-flow coefficient v2 of π− is shown to increase in the presence of an external magnetic field and the increment in v2 is found to depend on the evolution and the initial magnitude of the magnetic field.
We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi:10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi:10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to ∼50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.
Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first ever observed neutron star merger event GW170817.
Determining the phase structure of Quantum Chromodynamics (QCD) and its Equation of State (EOS) at densities and temperatures realized inside neutron stars and their mergers is a long-standing open problem. The holographic V-QCD framework provides a model for the EOS of dense and hot QCD, which describes the deconfinement phase transition between a dense baryonic and a quark matter phase. We use this model in fully general relativistic hydrodynamic (GRHD) simulations to study the formation of quark matter and the emitted gravitational wave signal of binary systems that are similar to the first ever observed neutron star merger event GW170817.
n this article we will focus on the appearance of the hadron-quark phase transition and the formation of strange matter in the interior region of the hypermassive neutron star and its conjunction with the spectral properties of the emitted gravitational waves (GWs). A strong hadron-quark phase transition might give rise to a mass-radius relation with a twin star shape and we will show in this article that a twin star collapse followed by a twin star oscillation is feasible. If such a twin star collapse would happen during the postmerger phase it will be imprinted in the GW-signal.
Hypermassive hybrid stars (HMHS) are extreme astrophysical objects that could be produced in the merger of a binary system of compact stars. In contrast to their purely hadronic counterparts, hypermassive neutron stars (HMNS), these highly differentially rotating objects contain deconfined strange quark matter in their slowly rotating inner region. HMHS and HMNS are both mestastable configurations and can survive only shortly after the merger before collapsing to rotating black holes. The appearance of the phase transition from hadronic to quark matter in the interior region of the HMHS and its conjunction with the emitted GW will be addressed in this article by focussing on a specific case study of the delayed phase-transition scenario that takes place during the post-merger evolution of the remnant. The complicated dynamics of the collapse from the HMNS to the more compact HMHS will be analysed in detail. In particular, we will show that the interplay between the spatial density/temperature distributions and the rotational profiles in the interior of the wobbling HMHS after the collapse generates a high-temperature shell within the hadron-quark mixed phase region of the remnant.
In this work, we discuss the dense matter equation of state (EOS) for the extreme range of conditions encountered in neutron stars and their mergers. The calculation of the properties of such an EOS involves modeling different degrees of freedom (such as nuclei, nucleons, hyperons, and quarks), taking into account different symmetries, and including finite density and temperature effects in a thermodynamically consistent manner. We begin by addressing subnuclear matter consisting of nucleons and a small admixture of light nuclei in the context of the excluded volume approach. We then turn our attention to supranuclear homogeneous matter as described by the Chiral Mean Field (CMF) formalism. Finally, we present results from realistic neutron-star-merger simulations performed using the CMF model that predict signatures for deconfinement to quark matter in gravitational wave signals.
Einstein’s theory of general relativity is often regarded as the best theory of gravity that we know. Yet, this theory often manifests itself under conditions where no symmetry is present and nonlinear dynamics dominates. I will discuss how these conditions are systematically accompanied by the restoration of some degree of symmetry. Hence, despite gravity appearing often under conditions devoid of symmetry, asymptotic solutions tend to restore symmetry.
We study in detail the nuclear aspects of a neutron-star merger in which deconfinement to quark matter takes place. For this purpose, we make use of the Chiral Mean Field (CMF) model, an effective relativistic model that includes self-consistent chiral symmetry restoration and deconfinement to quark matter and, for this reason, predicts the existence of different degrees of freedom depending on the local density/chemical potential and temperature. We then use the out-of-chemical-equilibrium finite-temperature CMF equation of state in full general-relativistic simulations to analyze which regions of different QCD phase diagrams are probed and which conditions, such as strangeness and entropy, are generated when a strong first-order phase transition appears. We also investigate the amount of electrons present in different stages of the merger and discuss how far from chemical equilibrium they can be and, finally, draw some comparisons with matter created in supernova explosions and heavy-ion collisions.
A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than 106 generic EOSs, we asses the validity of quasi-universal relations of neutron star properties for a broad range of rotation rates, from slow-rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modelling of the X-ray emission from the surface of rotating stars.
A considerable effort has been dedicated recently to the construction of generic equations of state (EOSs) for matter in neutron stars. The advantage of these approaches is that they can provide model-independent information on the interior structure and global properties of neutron stars. Making use of more than 106 generic EOSs, we assess the validity of quasi-universal relations of neutron-star properties for a broad range of rotation rates, from slow rotation up to the mass-shedding limit. In this way, we are able to determine with unprecedented accuracy the quasi-universal maximum-mass ratio between rotating and nonrotating stars and reveal the existence of a new relation for the surface oblateness, i.e., the ratio between the polar and equatorial proper radii. We discuss the impact that our findings have on the imminent detection of new binary neutron-star mergers and how they can be used to set new and more stringent limits on the maximum mass of nonrotating neutron stars, as well as to improve the modeling of the X-ray emission from the surface of rotating stars.
Determining the sound speed cs in compact stars is an important open question with numerous implications on the behavior of matter at large densities and hence on gravitational-wave emission from neutron stars. To this scope, we construct more than 107 equations of state (EOSs) with continuous sound speed and build more than 108 nonrotating stellar models consistent not only with nuclear theory and perturbative QCD, but also with astronomical observations. In this way, we find that EOSs with subconformal sound speeds, i.e., with cs 1 3 2 < within the stars, are possible in principle but very unlikely in practice, being only 0.03% of our sample. Hence, it is natural to expect that cs 1 3 2 > somewhere in the stellar interior. Using our large sample, we obtain estimates at 95% credibility of neutron-star radii for representative stars with 1.4 and 2.0 solar masses, R1.4 12.42 km 0.99 0.52 = - + , R2.0 12.12 km 1.23 1.11 = - + , and for the binary tidal deformability of the GW170817 event, 1.186 485 211 225 L = - ˜ + . Interestingly, our lower bounds on the radii are in very good agreement with the prediction derived from very different arguments, namely, the threshold mass. Finally, we provide simple analytic expressions to determine the minimum and maximum values of L˜ as a function of the chirp mass.
Post-merger gravitational-wave signal from neutron-star binaries: a new look at an old problem
(2023)
The spectral properties of the post-merger gravitational-wave signal from a binary of neutron stars encodes a variety of information about the features of the system and of the equation of state describing matter around and above nuclear saturation density. Characterising the properties of such a signal is an “old” problem, which first emerged when a number of frequencies were shown to be related to the properties of the binary through “quasi-universal” relations. Here we take a new look at this old problem by computing the properties of the signal in terms of the Weyl scalar ψ4. In this way, and using a database of more than 100 simulations, we provide the first evidence for a new instantaneous frequency, f ψ4 0, associated with the instant of quasi timesymmetry in the postmerger dynamics, and which also follows a quasi-universal relation. We also derive a new quasi-universal relation for the merger frequency f h mer, which provides a description of the data that is four times more accurate than previous expressions while requiring fewer fitting coefficients. Finally, consistently with the findings of numerous studies before ours, and using an enlarged ensamble of binary systems we point out that the ℓ = 2, m = 1 gravitational-wave mode could become comparable with the traditional ℓ = 2, m = 2 mode on sufficiently long timescales, with strain amplitudes in a ratio |h 21|/|h 22| ∼ 0.1 − 1 under generic orientations of the binary, which could be measured by present detectors for signals with large signal-to-noise ratio or by third-generation detectors for generic signals should no collapse occur.
Post-merger gravitational-wave signal from neutron-star binaries: a new look at an old problem
(2023)
The spectral properties of the post-merger gravitational-wave signal from a binary of neutron stars encodes a variety of information about the features of the system and of the equation of state describing matter around and above nuclear saturation density. Characterizing the properties of such a signal is an “old” problem, which first emerged when a number of frequencies were shown to be related to the properties of the binary through “quasiuniversal” relations. Here we take a new look at this old problem by computing the properties of the signal in terms of the Weyl scalar ψ4. In this way, and using a database of more than 100 simulations, we provide the first evidence for a new instantaneous frequency, y f0 4, associated with the instant of quasi-time-symmetry in the dynamics, and which also follows a quasi-universal relation. We also derive a new quasi-universal relation for the merger frequency f h mer, which provides a description of the data that is 4 times more accurate than previous expressions while requiring fewer fitting coefficients. Finally, consistent with the findings of numerous studies before ours, and using an enlarged ensemble of binary systems, we point out that the ℓ = 2, m = 1 gravitational-wave mode could become comparable with the traditional ℓ = 2, m = 2 mode on sufficiently long timescales, with strain amplitudes in a ratio |h21|/|h22| ∼ 0.1–1 under generic orientations of the binary, which could be measured by present detectors for signals with a large signal-to-noise ratio or by third-generation detectors for generic signals should no collapse occur.